## 16 Citations

### Invertibility Probability of Binary Matrices Team

- Mathematics, Computer Science
- 2008

This work conjecture that the invertibility probability of binary matrices monotonically increases as the size of the binary matrix increases is investigated, and a probable bound is obtained that would show that this conjecture is asymptotically true.

### Determinants of binary matrices achieve every integral value up to $\Omega(2^n/n)$

- Mathematics, Computer Science
- 2020

This work shows that the smallest natural number $d_n$ that is not the determinant of some $n\times n$ binary matrix is at least $c\,2^n/n$ for $c=1/201$. That same quantity naturally lower bounds…

### Computations associated with the resonance arrangement

- Mathematics
- 2021

The resonance arrangement An is the arrangement of hyperplanes in R n given by all hyperplanes of the form ∑ i∈I xi = 0, where I is a nonempty subset of {1, . . . , n}. We consider the characteristic…

### Singular 0/1-Matrices, and the Hyperplanes Spanned by Random 0/1-Vectors

- MathematicsCombinatorics, Probability and Computing
- 2006

It is proved that bounds on P_s(d) are equivalent to bounds on E(d), which is the expected number of 0/1-vectors in the linear subspace spanned by $d-1$ random independent 0/ 1-veters.

### Maximal determinants and saturated D-optimal designs of orders 19 and 37

- Mathematics
- 2011

A saturated D-optimal design is a {+1,−1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to…

### On Cycles in Random Graphs

- MathematicsArXiv
- 2010

The calculations indicate that the threshold for rapid growth in the number of Hamilton cycles in the GR graph is lower than in the ER graph, and throws some light on the question of the maximal determinant of symmetric $0/1$ matrices.

### Fighting the Symmetries: The Structure of Cryptographic Boolean Function Spaces

- Mathematics, Computer ScienceGECCO
- 2015

It is shown that symmetries yield additional information that may yield more effective search methods in the problem space of maximum nonlinearity problems for balanced Boolean functions, with implications for crossover and for distributional methods.

### Good pivots for small sparse matrices

- Computer ScienceCASC
- 2020

For sparse matrices up to size $8 \times 8$, optimal choices for pivot selection in Gaussian elimination are determined and they are slightly better than the pivots chosen by a popular pivot selection strategy.

### Row Space Cardinalities

- Mathematics
- 2006

AbstractLet ${\cal B}_n$ be the set of all $n\times n$ Boolean matrices. Let R(A) denote the row space of $A\in{\cal B}_n$, let ${\cal R}_n=\{r \mid r={\rm r}(A),\ A\in {\cal B}_n \}$, and let…

### Lower bound for Buchstaber invariants of real universal complexes

- Mathematics
- 2021

In this article, we prove that Buchstaber invariant of 4-dimensional real universal complex is no less than 24 as a follow-up to the work of Ayzenberg and Sun. Moreover, a lower bound for Buchstaber…

## References

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### Lectures on Polytopes

- Mathematics
- 1994

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward…

### An On-Line Version of the Encyclopedia of Integer Sequences

- Business
- 1994

A Handbook of Integer Sequences was published by Academic Press in 1973, and contained an annotated list of 2372 sequences arranged in lexicographic order. Since then a great deal of new material has…

### AN ALGORITHM FOR THE ORGANIZATION OF INFORMATION

- Computer Science
- 1963

The organization of information placed in the points of an automatic computer is discussed and the role of memory, storage and retrieval in this regard is discussed.

### Massive Computation as a Problem Solving Tool

- Proceedings of the 10th Congress of Yugoslav Matematicians
- 2001

### Massive Computation as a Problem Solving Tool

- Proceedings of the 10th Congress of Yugoslav Matematicians
- 2001

### On the determinant of (0, 1) matrices, Studia Sci

- Math. Hungarica
- 1967

### A Different Approach To Hadamard's Maximum Determinant Problem

- ICM
- 1998

### On the determinant of (0, 1) matrices

- Studia Sci. Math. Hungarica
- 1967